Equation of line in Straight lines

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Question

The base of an equilateral triangle is along the line given by $3 x + 4 y = 9$ . If a vertex of the triangle is $(1, 2)$ then the length of its side is

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Solution

The perpendicular distance from vertex $(1, 2)$ to the base $3 x + 4 y = 9$ is height h of the equilateral triangle
$\begin{matrix} h = |\frac{3 (1) + 4 (1) - 9}{\sqrt{3^{2} + 4^{2}}}| \\ = \frac{2}{5} \end{matrix}$
If a is the length of the side and h is height of an equilateral triangle then $a = \frac{2 h}{\sqrt{3}}$
Therefore, the length of the side is $a = \frac{4}{5 \sqrt{3}} = 0 .4618$

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

The base of an equilateral triangle is along the line given by 3x+4y=9 . If a vertex of the triangle is 1,2 then the length of its side is

The perpendicular distance from vertex 1,2 to the base 3x+4y=9 is height h of the equilateral triangle h=31+41−932+42=25 If a is the length of the side and h is height of an equilateral triangle then a=2h3Therefore, the length of the side is a=453=0.4618

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The base of an equilateral triangle is along the line given by $3 x + 4 y = 9$ . If a vertex of the triangle is $(1, 2)$ then the length of its side is